Alexa's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an angle of $20^\circ$, and traveled a distance of $3.4$ kilometers before she fell in a straight line perpendicular to the ground. How far from the skydiving center did Alexa land? Round your final answer to the nearest hundredth.
Solution: The strategy Model the situation as a right triangle. Determine the appropriate trigonometric ratio in order to find the missing side. Form an equation and solve for the missing side. Calculate the final result and round. Modeling as a right triangle This situation can be modeled by the following right triangle. The hypotenuse is $3.4\text{ km}$ and the angle on the left is $20^\circ$. We are asked to find the distance between the skydiving center and Alexa's landing point, which is the base of the triangle. ${20^{\circ}}$ $3.4$ $?$ Determining the appropriate trigonometric ratio We are given the measure of an angle and the length of the $C{\text{hypotenuse}}$. We are asked to find the side ${\text{adjacent}}$ to the given angle. The appropriate trigonometric ratio is therefore the $\text{cosine}$. Forming an equation and solving Denoting the missing side by $x$, we obtain the equation $\cos(20^\circ)=\dfrac{x}{3.4}$. Solving the equation, we get $x=3.4\cdot\cos(20^\circ)$. Evaluating this result in the calculator and rounding to the nearest hundredth, we get $x=3.19\text{ km}$. Summary Alexa landed $3.19$ kilometers from the skydiving center.